Simplify the following expression: $r = \dfrac{1}{8p} + \dfrac{4}{9p}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $8p$ and $9p$ $\lcm(8p, 9p) = 72p$ $ r = \dfrac{9}{9} \cdot \dfrac{1}{8p} + \dfrac{8}{8} \cdot \dfrac{4}{9p} $ $r = \dfrac{9}{72p} + \dfrac{32}{72p}$ $r = \dfrac{9 +32}{72p}$ $r = \dfrac{41}{72p}$